In magnetically confined plasma observed in space and fusion devices, density and temperature gradients drive instabilities and associated turbulence. This research clarifies the existence of cross-scale interactions between long-wave-length turbulence due to the dynamics of heavy ions and extremely short-wave-length turbulence due to the dynamics of light electrons. Such a multi-scale turbulence involving different two injection scales has been investigated by means of numerical simulations. We revealed that the mechanism of cross-scale interactions via sub-ion-scale structure, namely intermediate scale between electron and ion scales, which is generated by turbulent mixing or kinetic response of electrons.